On Lagrange interpolations and Kramer's sampling theorem associated with self-adjoint boundary value problems

Abstract

It is known that Kramer's sampling theorem and Lagrange-type interpolation generalize the celebrated Whittaker-Shannon-Kotel'nikov sampling theorem in two different directions; however, no direct connection between these two directions seems to be known. In this article we show that Kramer's sampling theorem gives nothing more than the Lagrange-type interpolations provided that the kernel function associated with Kramer's theorem arises from a self-adjoint boundary value problem with sample eigenvalues.